Pre- and postnatal development of topographic transformations in the brain [Elektronische Ressource] / von Urs Michael Bergmann

Sujets

• Physik

Informations

• Publié par: goethe_universitat_frankfurt_am_main
• Publié le: 01 janvier 2010
• Nombre de lectures: 39
• Langue: English
• Poids de l'ouvrage: 4 Mo

Extrait

Pre- and Postnatal Development of Topographic
Transformations in the Brain
DISSERTATION
zur Erlangung des Doktorgrades
der Naturwissenschaften
vorgelegt beim Fachbereich fur Physik
der Johann Wolfang Goethe-Universit at
in Frankfurt am Main
von
Urs Michael Bergmann
aus
Ludwigsburg
Frankfurt (2010)vom Fachbereich fur Physik der
Johann Wolfgang Goethe-Universit at als Dissertation angenommen.
Dekan: Prof. Dr. Dirk-Hermann Rischke
Gutachter: Prof. Dr. Christoph von der Malsburg, Prof. Dr. Jochen Triesch
Datum der Disputation: 4. April 2011Acknowledgements
First of all, special gratitude is dedicated to my supervisor, Christoph von der Malsburg,
for the positive and creative support throughout the development of my thesis. I would
like to thank Jochen Triesch, for being my second supervisor and for many interesting
discussions. Further, I would like to voice my appreciation for my colleagues at FIAS,
with its interdisciplinary background, that inspired and broadened my perspective even
beyond the already interdisciplinary eld of Neuroscience.
Special thanks goes to Gervasio Puertas, for fruitful collaboration and many interesting
discussions on the analytical parts of chapter 2. I am very grateful to Junmei Zhu for
the collaboration on turning chapter 4 into a paper. Further, I would like to thank Jenia
Jitsev, Gervasio Puertas and Junmei Zhu for proof-reading parts of the thesis. Additional
thanks goes to Claudius Gros, Andreas Braun, Dominik Heide, Andreea Lazar, Jan
Scholz, Christian Wol and Philip Wolfrum for many useful and inspiring discussions.
Finally, this thesis would not have been possible without the backing of my parents,
and especially my wife Gwendolyn’s enduring support, who gave me con dence and love
to overcome the more di cult days during my thesis.
34Contents
List of Figures 8
1 Introduction 9
1.1 Invariance in Vision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.1.1 Feature-based Invariance . . . . . . . . . . . . . . . . . . . . . . . . 10
1.1.2 Normalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.1.3 Bilinear Models and Modulatory Synapses . . . . . . . . . . . . . . 11
1.2 Topography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.2.1 Ontogeny of Topography . . . . . . . . . . . . . . . . . . . . . . . 14
1.3 Prenatal Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.4 Outline of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.5 Notational Conventions and List of Symbols . . . . . . . . . . . . . . . . . 17
2 A Gaussian Generative Model for the Ontogeny of Retinotopy 19
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2 An Analytically Solvable Model of Retinotopy . . . . . . . . . . . . . . . . 20
2.3 The Probabilistic Topographic Model . . . . . . . . . . . . . . . . . . . . . 26
2.3.1 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3 Self-Organization of Topographic Bilinear Networks for Invariant Recognition 31
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2 The H aussler System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.3 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.3.1 Input and Output Activities . . . . . . . . . . . . . . . . . . . . . . 38
3.3.2 Synaptic weight dynamics . . . . . . . . . . . . . . . . . . . . . . . 40
3.3.3 WTA Control Unit Selection . . . . . . . . . . . . . . . . . . . . . 41
3.3.4 Equilibrium Solution of the Neural Fields . . . . . . . . . . . . . . 43
3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.4.1 Quantitative Characterization of RPF Development . . . . . . . . 47
3.4.2 Signal Processing Analysis of Final RPFs . . . . . . . . . . . . . . 49
3.4.3 Speci city Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.4.4 Complex Inputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.5 2D Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.6 Probability-based Scale Organization . . . . . . . . . . . . . . . . . . . . . 56
53.7 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.8 Future Perspectives and Conclusion . . . . . . . . . . . . . . . . . . . . . 60
4 Multi-layer Organization of Translations 63
4.1 Model Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.1.1 Derivation of the Weight Cooperation from Local Hebbian Rules . 66
4.2 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.3 Conclusion and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5 Slowness yields consistent Features across Transformations in a Bilinear Model 73
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.2 The Bilinear Topographic Model . . . . . . . . . . . . . . . . . . . . . . . 75
5.2.1 Topography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.2.2 Slowness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.2.3 Dynamics and Learning Rule . . . . . . . . . . . . . . . . . . . . . 78
5.3 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.3.1 Natural Inputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.3.2 Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.3.4 Face experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6 Conclusion and Outlook 93
A Gabor Fitting of Generative Fields 95
Bibliography 97
Index 109
Zusammenfassung in deutscher Sprache 111
Lebenslauf 117
6List of Figures
1.1 Measured and simulated retinal waves. . . . . . . . . . . . . . . . . . . . . 15
2.1 Correlation structure of neuronal activity in retinal waves and inferotem-
poral cortex. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2 Converged mappings of the Gaussian retinotopy model. . . . . . . . . . . 29
3.1 Control units implement transformations. . . . . . . . . . . . . . . . . . . 33
3.2 Cooperation and competition in the H aussler system. . . . . . . . . . . . . 36
3.3 Training of control units employing active regions. . . . . . . . . . . . . . 38
3.4 Schematic active inputs regions. . . . . . . . . . . . . . . . . . . . . . . . . 45
3.5 Control unit weights at an intermediate stage and in their converged states. 46
3.6 Time development of input speci city and synaptic spread. . . . . . . . . 48
3.7 Final transformation scales and their time development. . . . . . . . . . . 49
3.8 Average output RPFs and their transfer functions. . . . . . . . . . . . . . 50
3.9 Analysis of the norm of the receptive-projective elds. . . . . . . . . . . . 53
3.10 2D receptive-projective elds at an intermediate stage. . . . . . . . . . . . 55
3.11 2D receptive-projective elds in their converged state. . . . . . . . . . . . 57
3.12 Probability-based Scale Organization. . . . . . . . . . . . . . . . . . . . . 58
4.1 Link interactions of control units that lead to the self-organization of
di erent translations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.2 Shifter Circuit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.3 Converged weight con gurations for di erent modes of the model. . . . . 68
4.4 Synaptic spread development for the di erent modes of the model. . . . . 69
4.5 Final tranformations on a shifter circuit. . . . . . . . . . . . . . . . . . . . 71
5.1 Sanger’s rule applied to natural inputs. . . . . . . . . . . . . . . . . . . . . 74
5.2 Experimental IT responses and used probability densities. . . . . . . . . . 75
5.3 The bilinear generative model. . . . . . . . . . . . . . . . . . . . . . . . . 77
5.4 Natural image patches. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.5 Converged generative weights for a single control unit. . . . . . . . . . . . 82
5.6 Simulation result and Gabor t. . . . . . . . . . . . . . . . . . . . . . . . . 83
5.7 Illustration of the color coding of the generative elds. . . . . . . . . . . . 83
5.8 Control unit responses on disjoint input patterns. . . . . . . . . . . . . . . 84
5.9 Histograms of the output units. . . . . . . . . . . . . . . . . . . . . . . . . 85
75.10 Final generative weights for two control units. . . . . . . . . . . . . . . . . 86
5.11 Topographic maps extracted from the generative weights. . . . . . . . . . 87
5.12 FERET Face images. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.13 Generative Weights learned from FERET data. . . . . . . . . . . . . . . . 89
81 Introduction
A long standing mystery surrounding the functioning of the brain is how it manages to
handle the enormous variety of di erent neuronal activity patterns and organize these so
that they are related in a meaningful way. These patterns can be sensory, motor, but
also internally generated patterns. A major